A Complete Map of Conditional Knowledge Bases in Different Normal Forms and Their Induced System P Inference Relations Over Small Signatures
Christoph Beierle, Jonas Philipp Haldimann, Steven Kutsch · Proceedings of the ... International Florida Artificial Intelligence Research Society Conference · 2021
Conditional knowledge bases consisting of qualitativeconditionals play a predominant role in knowledge representationand reasoning. In this paper, we develop a full map of allconsistent conditional knowledge bases over a small signature indifferent normal forms. We introduce two new normal formsthat take the induced system P inference relation into account,the system P normal form (SPNF) and the renaming SPNF(ρSPNF) considering additionally renamings of theunderlying signature. For a two-element signature, we systematicallygenerate and compare all consistent knowledge bases in ANF,RANF, SPNF, and their renaming counterparts, as well as allcomplete system P inference relations induced by conditionalknowledge bases.